{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JRLD5KIHYVZB6ZGKCWVI7USLTQ","short_pith_number":"pith:JRLD5KIH","canonical_record":{"source":{"id":"2409.10238","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-09-16T12:40:35Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4e79a95b283d3ddbce441f19b688388ccd7027f84a27905320fd211973972a2b","abstract_canon_sha256":"cd20a688cdf5c670738924b25ff8e22a23b129caf7146b12121bfdd34e494ae0"},"schema_version":"1.0"},"canonical_sha256":"4c563ea907c5721f64ca15aa8fd24b9c0adfca4eeffe060df520bfbd8016c218","source":{"kind":"arxiv","id":"2409.10238","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.10238","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"arxiv_version","alias_value":"2409.10238v2","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.10238","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"pith_short_12","alias_value":"JRLD5KIHYVZB","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"pith_short_16","alias_value":"JRLD5KIHYVZB6ZGK","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"pith_short_8","alias_value":"JRLD5KIH","created_at":"2026-07-05T10:43:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JRLD5KIHYVZB6ZGKCWVI7USLTQ","target":"record","payload":{"canonical_record":{"source":{"id":"2409.10238","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-09-16T12:40:35Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4e79a95b283d3ddbce441f19b688388ccd7027f84a27905320fd211973972a2b","abstract_canon_sha256":"cd20a688cdf5c670738924b25ff8e22a23b129caf7146b12121bfdd34e494ae0"},"schema_version":"1.0"},"canonical_sha256":"4c563ea907c5721f64ca15aa8fd24b9c0adfca4eeffe060df520bfbd8016c218","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:43:01.420835Z","signature_b64":"AsoN3mMOTlIGz6fyt1sqMfLUOGQUwPzpc1duat7wF2D9e/P0KBQZQJRHruMjW1AZI/t5McQAVQBEz2Qc7I3cDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c563ea907c5721f64ca15aa8fd24b9c0adfca4eeffe060df520bfbd8016c218","last_reissued_at":"2026-07-05T10:43:01.420398Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:43:01.420398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.10238","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:43:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1U+2HilBK5HN7JC6wcnP6MCSTTWO2Ado0UJ6hrTB2ZudWNvO+Ulz+s82ohdnPbAjSBOeFTSUdiBaP3dryXC8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:59:10.281900Z"},"content_sha256":"df402fa31419c0a1523797b8ba3f80be80d7091875e6dea9ae487b6172283809","schema_version":"1.0","event_id":"sha256:df402fa31419c0a1523797b8ba3f80be80d7091875e6dea9ae487b6172283809"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JRLD5KIHYVZB6ZGKCWVI7USLTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumeration of Rational Cuspidal Curves via the WDVV equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Anantadulal Paul, Apratim Choudhury, Indranil Biswas, Ritwik Mukherjee","submitted_at":"2024-09-16T12:40:35Z","abstract_excerpt":"We give a conjectural formula for the characteristic number of rational cuspidal curves in the projective plane by extending the idea of Kontsevich's recursion formula (namely, pulling back the equality of two divisors in the four pointed moduli space). The key geometric input that is needed here is that in the closure of rational cuspidal curves, there are two component rational curves which are tangent to each other at the nodal point. While this fact is geometrically quite believable, we haven't as yet proved it; hence our formula is for the moment conjectural. The answers that we obtain ag"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.10238","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.10238/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:43:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfNuzDcWq4quz2cIE6xGml8hH/FRG3La0sloEiOZikZC6eJo0ROO3LuMdHWKvOcXNCdz7X03J1aWflMFwg4EBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:59:10.282848Z"},"content_sha256":"c58476845ed823050b50fb773d7d297b578eef4f5cd5d963e5776e3d22d5e611","schema_version":"1.0","event_id":"sha256:c58476845ed823050b50fb773d7d297b578eef4f5cd5d963e5776e3d22d5e611"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JRLD5KIHYVZB6ZGKCWVI7USLTQ/bundle.json","state_url":"https://pith.science/pith/JRLD5KIHYVZB6ZGKCWVI7USLTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JRLD5KIHYVZB6ZGKCWVI7USLTQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T11:59:10Z","links":{"resolver":"https://pith.science/pith/JRLD5KIHYVZB6ZGKCWVI7USLTQ","bundle":"https://pith.science/pith/JRLD5KIHYVZB6ZGKCWVI7USLTQ/bundle.json","state":"https://pith.science/pith/JRLD5KIHYVZB6ZGKCWVI7USLTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JRLD5KIHYVZB6ZGKCWVI7USLTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JRLD5KIHYVZB6ZGKCWVI7USLTQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cd20a688cdf5c670738924b25ff8e22a23b129caf7146b12121bfdd34e494ae0","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-09-16T12:40:35Z","title_canon_sha256":"4e79a95b283d3ddbce441f19b688388ccd7027f84a27905320fd211973972a2b"},"schema_version":"1.0","source":{"id":"2409.10238","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.10238","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"arxiv_version","alias_value":"2409.10238v2","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.10238","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"pith_short_12","alias_value":"JRLD5KIHYVZB","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"pith_short_16","alias_value":"JRLD5KIHYVZB6ZGK","created_at":"2026-07-05T10:43:01Z"},{"alias_kind":"pith_short_8","alias_value":"JRLD5KIH","created_at":"2026-07-05T10:43:01Z"}],"graph_snapshots":[{"event_id":"sha256:c58476845ed823050b50fb773d7d297b578eef4f5cd5d963e5776e3d22d5e611","target":"graph","created_at":"2026-07-05T10:43:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.10238/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a conjectural formula for the characteristic number of rational cuspidal curves in the projective plane by extending the idea of Kontsevich's recursion formula (namely, pulling back the equality of two divisors in the four pointed moduli space). The key geometric input that is needed here is that in the closure of rational cuspidal curves, there are two component rational curves which are tangent to each other at the nodal point. While this fact is geometrically quite believable, we haven't as yet proved it; hence our formula is for the moment conjectural. The answers that we obtain ag","authors_text":"Anantadulal Paul, Apratim Choudhury, Indranil Biswas, Ritwik Mukherjee","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-09-16T12:40:35Z","title":"Enumeration of Rational Cuspidal Curves via the WDVV equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.10238","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:df402fa31419c0a1523797b8ba3f80be80d7091875e6dea9ae487b6172283809","target":"record","created_at":"2026-07-05T10:43:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cd20a688cdf5c670738924b25ff8e22a23b129caf7146b12121bfdd34e494ae0","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-09-16T12:40:35Z","title_canon_sha256":"4e79a95b283d3ddbce441f19b688388ccd7027f84a27905320fd211973972a2b"},"schema_version":"1.0","source":{"id":"2409.10238","kind":"arxiv","version":2}},"canonical_sha256":"4c563ea907c5721f64ca15aa8fd24b9c0adfca4eeffe060df520bfbd8016c218","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c563ea907c5721f64ca15aa8fd24b9c0adfca4eeffe060df520bfbd8016c218","first_computed_at":"2026-07-05T10:43:01.420398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:43:01.420398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AsoN3mMOTlIGz6fyt1sqMfLUOGQUwPzpc1duat7wF2D9e/P0KBQZQJRHruMjW1AZI/t5McQAVQBEz2Qc7I3cDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:43:01.420835Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.10238","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df402fa31419c0a1523797b8ba3f80be80d7091875e6dea9ae487b6172283809","sha256:c58476845ed823050b50fb773d7d297b578eef4f5cd5d963e5776e3d22d5e611"],"state_sha256":"7a3f548443416dafae51817e85a9f2b912b5f5f202077034c418143c00219f69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3apYE2TwX+cIMoVp1XPyr7jLNNFgncXmBZ74NGP2x2Ga1dj4ySxYvGqiZlod8KRMnCwm38nwgDmONcEk654XCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T11:59:10.289572Z","bundle_sha256":"2a4d94f0223ec049800431036b202ef3c5f9d49405717f8b5105d651e3af6b47"}}